The term "white elephant" is commonly used to describe a useless or burdensome possession. In Asian folklore it is said that white elephants were sacred, but because of their sanctity could not be used to perform any manual labor. Thus, the elephant became useless to its possessor and quite expensive to maintain. The term white elephant is still in use today as friends or office workers gather and give and receive white elephant gifts, mainly just for the fun of it. Most people have these useless gifts around the house somewhere.
In Hemingway's short story, Jig refers to the hills in the distance as looking like white elephants in her conversation with the man. In this case, the term is a veiled reference to the unborn child she is carrying. It becomes a way for the idea of abortion to be introduced into the story. That the girl believes the hills look "lovely" seems to indicate she wants to keep the child. A little later she even says they don't resemble white elephants, further strengthening her argument that they should keep the baby. The man seems to disregard this comment and continues to argue for an abortion.